Proof of $(I-C)^{-1}\leq \|I\| + \|C\| + \|C\|^2 + \cdots$ Using Matrix C

[flop]

Given that C is a matrix and that I - C is invertible, could someone show me the following?

\|(I - C)^{-1}\| \leq \|I\| + \|C\| + \|C\|^2 + \cdots

 

[Hurkyl]

That formula looks awfully similar to:

<br /> \frac{1}{1 - x} = 1 + x + x^2 + x^3 + \cdots<br />

Maybe the method of proof is similar?

 

[flop]

got it! thank you hurky